Definition of Double-suited
Double-suited means cards that are "double-assorted". The expression is mostly used in Omaha. In Hold'em, when you receive AK in spade preflop, it is said that you have suited cards (matching, of the same suit). The expression is also used on Omaha for matching cards. And since you receive 4 cards on Omaha, you may receive AK in spades and AK in hearts, for example. In that case, you will be called a "Double-suited" hand. Regardless of the combination, if you receive 2 cards of one suit and 2 cards of another suit, you will have a Double-suited hand.
Suited vs. Double-suited to Omaha and Fairness
Unlike Hold'em, where it's good news to receive cards that are both of the same suit, at Omaha, it's bad news. If you receive 4 cards in spades or 4 cards in hearts at Omaha, it's bad news because you know you're less likely to hit your suit. On the other hand, if you have a Double-suited hand, that's good news. The fact that your hand is Double-suited will add to your equity. For example, if you have a hand like 5-6-7-8 odd, you will have 42% equity against a random hand. But if you have 5-6-7-8 double suited, you will now have 49% equity against a random hand.